All of the higher order hedrons are just split up versions of certain base shape. What you do is smooth the base shape for a higher order shape.
Please note not all face counts are possible for example 7 is not likewise 10 is not either*. I would need to count to see if 50 sided is possible ( anything above d20 is offcourse no longer a hedra if you talk of real dice, really for example a d100 is just a ball really you could do the stopping by making gooves inside the shape for a stopper shape, and thus above a certain number you could construct any number of faces without needing to make mathematically right number or herda sides)
Also note the highest number of platonic solids is not the dodecahedron its the icosahedron (which has 20 sides) They are not listed in growing order but rather edge counts.
So e for example a
d10 is not a really in the family of hedra really its a 5 segmented sweep, you could make any 2 divisible die this way but its not practical above certain numbers
d16 is tetrahedra face split into 4 (a triangle split into four is called a lienear smooth in maya)
d20 is just simply a icosahedron
d24 can be obtained by splitting a dodecahedron
d32 is a octaherda with each face split into 4
d60 smoothed icosahedron or a poked dodecahedron
d80 is a icosahedron each triangle split into 4 etc etc
Please note all of th hiher order splits do not create a even spacing for e faces unless you spherize the result and even then some do not work out perfectly. Without iterating the spacing
*yes d7 and d10 do exist but its not so much about known headra its about a wider search for them has been done. No simple formula exists.